Question

6. ABCD is a rhombus. Find the value of y.

Answer 1

Answer:

y = 42°

Step-By-Step Explanation:

since it is a rhombus, the 4 angles next to the line AC are going to be the same (48°)

Since those 4 angles are 48°,

48° × 4 = 192°

Since all quadrangles (quadrilaterals) have combined angle of 360°,

360° - 192° = 168°

Since the 4 other angles must add up to 168°,

168° ÷ 4 = 42°

Since the 4 angles around the line BD are 42° each,

y = 42°

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Answer 2

Answer:

$y=42$

Skills needed: Rhombus Geometry

1) We need to understand a property of rhombi (plural of rhombus) that is important in this problem.

---> $\overline{AC}$ is a diagonal in the rhombus.

---> $\overline{BD}$ is also a diagonal in the rhombus.

- In a rhombus, the diagonals are always perpendicular to each other.

---> Let's make the point of intersection of the diagonals as Point E.

$\angle BEC=90$

---> This angle is needed to solve the problem for y.

2) Using triangle properties:

---> The sum of interior angles of a triangle equal 180.

- Take $\triangle{BEC$, which has 3 angles:

$\angle{BEC}, \angle{ECB}, \angle{CBE}$

$\angle{BEC+\angle{ECB + \angle{CBE=180$

$\angle{BEC=90$ due to rhombus diagonal property

$\angle{ECB=48$ which is given

$\angle{EBC=y$ (what we are trying to solve for)

Let's plug in!

3) $90+48+y=180 \\ 138+y=180 \\ y=42$

y equals 42